1.

The Correct Answer is (B) — You can solve the equation 4x + 7 = 15 for x by subtracting 7 from both sides and then dividing by 4 to get x = 2. Since x = 2, 6x – 5 = 6(2) – 5 = 12 – 5 = 7.

2.

The Correct Answer is (C) — If Victoria rides for k kilometers, the cost of her ride will be 3.25 + 0.75k. Since the cost of her ride is 12.25, you can write 3.25 + 0.75k = 12.25 and solve for k:

3.

The Correct Answer is (B) — The mean of a set of numbers can be found by adding up all of the numbers and then dividing by the number of numbers. In this case, the mean is equal to .
If you chose (A), you may have found the median of the data set. If you chose (C), you may have found the mode of the data set.

4.

The Correct Answer is (C) — You can simplify the expression by grouping like terms: 3x – 11 + 11x + 74 = 14x + 63. Now, substitute x=y/2 into the first expression to find an equivalent expression in terms of y: 14(y/2) + 63 = 7y + 63 = 7(y + 9).

5.

The Correct Answer is (B) — You can read the graph to see that the number of hamburgers sold by 10:00 PM is 500, and the number of hamburgers sold by 6:00 PM is 350. To find the number of hamburgers sold between 6:00 PM and 10:00 PM you can subtract these to get 500 – 350 = 150.
If you got (C), you may have found the number of burgers sold by 6:00 PM. If you got (D), you may have found the number sold by 10:00 PM.

6.

The Correct Answer is (B) — The speed at which hamburgers are being sold is the number sold divided by the length of the time period. Between 8:00 AM and 10:00 AM, the restaurant was selling 50/2 = 25 hamburgers per hour. Between 10:00 AM and 2:00 PM, the restaurant was selling 200/4 = 50 hamburgers per hour. Between 2:00 PM and 6:00 PM, the restaurant was selling 100/4 = 25 hamburgers per hour. Between 6:00 PM and 10:00 PM, the restaurant was selling 150/4 = 37.5 hamburgers per hour. Of these, the period with the highest rate is 10:00 AM to 2:00 PM.

7.

The Correct Answer is (D) — From reading the table, you know that 24 out of the 40 employees surveyed drink coffee. Because this is a large enough sample size, this result can be reasonably extended to the entire office, and you can expect that the same proportion of the entire office will drink coffee: .

8.

The Correct Answer is (D) — Liu needs to run the motor at a speed within 20 kilometers per hour of 100 kilometers per hour. You can write this as 100 – 20 ≤ x ≤ 100 + 20, where x is the speed he runs the motor at. This simplifies to 80 ≤ x ≤ 120. Because the question says “within at most 20 kilometers per hour”, you know to include the numbers 80 and 120 in the solution set, because these are acceptable speeds at which to run the motor. This tells you to use the ≤ symbol instead of the < symbol.
If you chose (C), you most likely misinterpreted the phrase “at most” in the question.

9.

The Correct Answer is (A) — In general, the results of a survey can only be extended to the population from which the sample was drawn. In this case, since only children in the neighbourhood of the arcade were surveyed, the results can only be extended to children from the same neighbourhood.
(B) is incorrect; no parents were surveyed and so the results cannot be extended to predict how other parents will answer. (C) is incorrect; children from other parts of the world may have drastically different opinions about which superhero is their favourite. (D) is incorrect; no comic book writers were surveyed.

10.

The Correct Answer is (B) — You can plug the slope, m = 1/4, and the point (8, 5) into the slope-intercept equation of a line, y = mx + b, to solve for b, the y-intercept:

11.

The Correct Answer is (A) — To find the year in which the population was estimated to be 400,000, find the 400 on the y-axis (representing population in thousands of people) and trace the horizontal line over to where it meets the line of best fit. Then, trace downward from there to find the x-value that corresponds to 400,000. This x-value is between 1990 and 2000, and is slightly closer to 1990, so the best answer choice is 1993.

12.

The Correct Answer is (D) — The slope of a line represents the rate of change in the y-values compared to the x-values. In this case, the slope represents the increase in population by the thousands each year, so (D) is correct. You can check this answer by reading the chart to see that City H has in fact been growing by approximately 100,000 people every 10 years, or 10,000 people each year. If you chose (C), you may have misread the x-axis of the chart.

13.

The Correct Answer is (A) — Since a music student is being selected at random, there are 175 possible students that could be chosen. Of these 175, 77 are female. Therefore, there is a 77/175 chance of a female being selected.
If you chose (B), you may have calculated the probability of choosing a female music student when picking a random Grade 9 student. If you chose (C), you may have calculated the probability that a randomly selected music student will be male. If you chose (D), you may have found the probability that a randomly selected Grade 9 student will be a music student.

14.

The Correct Answer is (A) — In the real tower, as seen in the diagram, the ratio of the height to the side length of the base is 300:75 = 4:1. Stan’s tower will need to have that same ratio to be to scale, so you can set up the following proportion and solve for base length, b:

15.

The Correct Answer is (D) — The correct way to design a trial is to choose the control group and the test group randomly. This will make the results of the trial meaningful.
(A), (B), and (C) are incorrect; these methods will bias the results of the study and will not lead to useful or meaningful results.

16.

The Correct Answer is (C) — You can find the slope of this line by dividing the difference in y-values by the difference in x-values: . Since the y-intercept is marked on the graph, you know it is –6. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept, so in this case the equation is y = 3/2 x – 6.

17.

The Correct Answer is (B) — You can test all the answers and see if they lead to a word count for the essay that is within the constraints of Andre’s assignment. If he writes for 2 hours, he will have written , which is not enough. If he writes for 2 hours and 10 minutes, he will have written 1040 words, which is within the guidelines of the assignment. If he writes for 3 hours and 10 minutes, he will have written 1520 words, which is too many. If he writes for 3 hours and 30 minutes, he will have written 1680 words, which is also too many. Therefore, (B) is the only answer that works.

18.

The Correct Answer is (A) — It is easy to tell from the symmetry of the diagram that both histograms show data with a mean of 30. If you aren’t sure, you can calculate the mean for each of them by adding up the rainfall on each day and dividing by the number of days, 58. However, the data for City X has a greater standard deviation because the data is more spread out; notice that the x-axis goes from 0 to 60 mm instead of 15 to 45 mm. Since the cities have the same mean but City X has a greater standard deviation, (A) is the correct answer.

19.

The Correct Answer is (D) — It is possible to quickly eliminate (A) and (B) by noting that the parabola in the figure opens upward, while the parabolas in (A) and (B) open downward. Then, you can plug x = –1 into the remaining answer choices and see what value of f (–1) is obtained. In (C), f (–1) = –4, so this is incorrect. In (D), f (–1) = –30, which roughly matches the diagram, so it is correct.

20.

The Correct Answer is (B) — An account that pays a certain percentage of the current balance each year leads to exponential growth of the account. Of the options, (B) is the only one that represents an exponential function.
(A) is incorrect; this is a linear function. (C) is incorrect; this is a constant function. (D) is incorrect; this is another linear function.

21.

The Correct Answer is (A) — First, notice that the small triangle and the large triangle are similar, since they are both right-angled and share an acute angle, meaning their angles have the same measures. This means that the ratios between each triangle’s side lengths are the same. You can set up the following proportion and solve:

22.

The Correct Answer is (C) — You can rearrange the equation to get , and then take the square root of both sides to get , and since

23.

The Correct Answer is (C) — Simplify the first equation using exponent rules:

Amazingly, the value of x + 2y has appeared!

24.

The Correct Answer is (C) — You know from the question that the water level rises at a constant rate. Because the water level is 3 feet 6 inches at 8:20 and 3 feet 9 inches at 8:40, you know that the water level is rising at a rate of 3 inches every 20 minutes. Since 10:00 is 4 × 20 minutes later than 8:40, the water level increases by 4 × 3 = 12 inches. The water level is 3’9” at 8:40, so the water level will be 3’9” + 12” = 4’9” at 10:00.

25.

The Correct Answer is (C) — To start, plug in m = 6 into the first equation, and solve for k:

You can see that k = 3 or k = –3. Of these, only 3 appears as an answer choice.

26.

The Correct Answer is (D) — Every student in the class owns a cat, a dog, both, or neither. Since 25% of the students in the class own neither a cat nor a dog, you know that 75% own at least one pet. The total number of students who own at least one pet is 7 + 9 + 5 = 21, so 21 students make up 75% of the class. You can then write 21 = 0.75x, where x is the number of students in the class, and solve to get x = 28.
If you got (A), you may have found the number of students who owned at least one pet and stopped there.

27.

The Correct Answer is (A) — First, substitute the value of 2y in the first equation with 4x – 13 from the second equation. Then, solve for x:

Once you know x = 8, you can substitute this into either of the two original equations to find y:

Therefore, the solution (x, y) is (8, 19/2).

28.

The Correct Answer is (B) — The length of the shaded line segment is equal to the length of the half-diagonal of the square (i.e. the distance from the center of the square to the corner) minus the radius of the circle. To find the radius of the circle, note that the side length of the square is two units, and the square is also two radii wide. Therefore, the radius of the circle is 1. To find the length of the half-diagonal of the square, you can use the right-angled triangle drawn with the dotted line. Since we know the radius is 1, and the top part of the right triangle is equal to half of the side length of the square, this is a 1-1-√2 triangle, meaning that the half-diagonal is √2. Finally, the length of the half-diagonal minus the radius is √2 – 1.

29.

The Correct Answer is (C) — To find the value of x at which they collide, you can set the two paths equal and solve:

You have found two values for x, but the only solution represented in the answer choices is x = 8.

30.

The Correct Answer is (B) — If there is only one possible solution for x, then that means the discriminant, b2 – 4ac, is equal to zero and x = . Instantly, you can see that II is true. To see that I is also true, solve for b:

Finally, III states that x is equal to the square root of the discriminant, which is false by the Quadratic Formula. Therefore, only I and II are true.

31.

The Correct Answer is (4.5 or 9/2) — Time is equal to distance divided by speed, so the time the trip will take is = 4.5 h.

32.

The Correct Answer is (9) — Since you are given a point on the line, you can just substitute this point for x and y, and solve for k: 5 = 2(7) - k, so k = 9.

33.

The Correct Answer is (195) — You can use unit conversion to solve this problem as follows:

34.

The Correct Answer is (0.625 or 5/8) — You want to find when y = 0, which is when |8x – 5| = 0. Solving this gives x = 5/8 = 0.625.

35.

The Correct Answer is (3) — The day before the holiday, Lucy worked 8 hours at regular pay, which is $9 per hour, and 120 minutes (2 hours) overtime, which pays (1.5)($9) = $13.5 per hour. Therefore, on this day, she made (9 × 8) + (13.5 × 2) = 72 + 27 = 99 dollars. To earn $153 in total, she needs to earn $153 – $99 = $54 on the next day. Since this next day is a holiday, she earns double her normal pay, which is (2)($9) = $18 per hour. To earn $54, then, she must work $54 ×(1 h)/$18 = 3 hours.

36.

The Correct Answer is (3) — To solve this question, you want to rearrange the equation so it is in standard form, (x + k)2 + (y + h)2 = r2, where r is the radius. The first step is to complete the square, as follows.

Since the standard form of a circle has ron the right side of the equation, you can see that r2 = 9, meaning that r = 3.

37.

The Correct Answer is (15) — By looking at the graph, the line is at its lowest point on the 15th, when it is around 2.3 dollars.

38.

The Correct Answer is (80) — The stock price on April 2nd is $2.50, and the stock price on April 5th is $4.50. This represents a percent increase of .